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Gilman had been advised to start off with an outstanding
classicist and the best mathematician he could afford as the
nucleus of his faculty. All the rest would follow, he was told,
and it did* Sylvester at last got a job where he might do prac-
tically as he pleased and in which he could do himself justice.
In 1876 he again crossed the Atlantic and took up his professor-
ship at Johns Hopkins. His salary was generous for those days,
five thousand dollars a year. In accepting the call Sylvester
made one curious stipulation; his salary was *to be paid in gold'.
Perhaps he was thinking of Woolwich, which gave him the
equivalent of $2750.00 (plus pasturage), and wished to be sure
that this time he really got what was coming to him, pension or
no pension.
The years from 1876 to 1883 spent at Johns Hopkins were
probably the happiest and most tranquil Sylvester had thus far
known. Although he did not have to 'fight the world' any longer
he did not recline on his honours and go to sleep. Forty years
seemed to fall from his shoulders and he became a vigorous
young man again, blazing with enthusiasm and scintillating
with new ideas. He was deeply grateful for the opportunity
Johns Hopkins gave him to begin his second mathematical
(career at the age of sixty-three, and he was not backward in
expressing his gratitude publicly, in his address at the Com-
memoration Day Exercises of 1877.
In this Address he outlined what he hoped to do (he did it) in
his lectures and researches.
"There are things called Algebraical Forms. Professor Cayley
calls them Quantics. [Examples: && + 2baey + ct/a, aa? -f $bx*y
+ Zcactj* -f dt^\ the numerical coefficients 1,2,1 in the first,
1,8,3,1 in the second, are binomial coefficients, as in the third
and fourth lines of Pascal's triangle (Chapter 5); the next in
order would be a:4 -f 4as*y + 6a?V -f te/3 + #*]. They are not,
properly speaking, Geometrical Forms, although capable, to
some extent, of being embodied in them, but rather schemes of
process, or of operations for forming, for calling into existence,
as it were, Algebraic quantities*
"To every such Quaatic is associated an infinite variety of
otfcer forms that may be regarded as engendered from and